Hi again Dave,
I want to clarify the 6 foot stream of spray from the accelerator pump nozzle.
https://www.boats.net/catalog/honda.../bf15dk3-lha-2007-and-later/carburetor-manual
Number 14 in the MANUAL CHOKE carb parts link above is the accelerator pump. It shoots a burst of fuel out of a tiny nozzle drilled into a small brass tube that juts out into the carb throat at the entrance to the Venturi.
When cleaning one of these it's important that you locate the passageway that feeds that tube and make sure it is clean. You must remove the float chamber and then determine the passage in it that the accelerator pump piston pushes fuel through to the main body when the piston is stroked downwards. The passage in the float chamber will, of course, match up with the nozzle feed passage when the chamber is mated to the main body. Spraying cleaner into that passage should have fluid coming out of the nozzle. If not, the nozzle is likely totally plugged.
Find a way to prop open the throttle plate fully. I use a small, pocket screwdriver jammed in the linkage after I've opened the throttle fully. With the throttle plate propped open, you can look through the Venturi from the rear of the carb and see the accelerator pump nozzle and tube.
Use the plastic straw on your can of cleaner and carefully place it directly over the nozzle orifice and give it a shot of cleaner. Fluid should flow out of the passageway I told you to locate earlier. If no flow occurs, don't worry, I haven't seen one yet that won't clear if you keep after it.
Try spraying fluid into the passage to get fluid to exit the nozzle. This is where you will eventually want to see the 6' stream coming out past the throttle plate at the rear of the carb.
BE CAREFUL AND WEAR EYE PROTECTION while doing this!
If the stream is weak or non existant, repeat by placing the straw over the nozzle and "back flushing" the tube and then go back to the tube feed inlet and spray there again.
Keep doing this until you get get the long stream I describe. It can take many tries and a can of fluid or more to clear a badly clogged tube.
Also, while you have the throttle plate propped completely open, you will be able to see and access ALL of the fuel feed orifices at the top of the carb throat. Use the spray straw to cover each orifice and back flush each, one at a time. This is best done with the jet set tube and idle mixture screw removed. You will see fluid coming out of the idle mix cavity when you hit the idle orifice and you'll see fluid flow from the main passage where the jet set mounts when you spray the transition and full speed orifices respectively.
As a matter of fact, your full speed orifice may be plugged judging by the symptom you describe so this is a good thing to try before loading the parts shotgun.
After back flushing the orifices, you can foreflush the passages by inserting the straw where you saw fluid exiting when spraying the orifices. The fluid comes out of several places at once when doing all this and I've learned to use my fingers and thumb to block the fluid from as many "exits" as possible to increase the spray cleaning power when working on a particular circuit.
I hope this helps you but I won't blame you if you're a bit confused.
Keep us posted.